The invention relates to a fault-detection apparatus for detecting the presence of a fault in an electrical power line, and in particular, but not exclusively, a multi-phase underground-cable power line and a composite line including an underground-cable power line.
Fault-detection arrangements are known in which the line being monitored for faults is modelled simply as series inductance and resistance elements, any shunt capacitance that may exist between the line and any other line or earth being ignored. Such a line will normally be an overhead power line. FIG. 1 shows this scenario, in which a line 10 is considered to have a lumped impedance Z, consisting of an inductive reactance XL associated with an inductive component L, and a resistance RL and is monitored in terms of voltage Vr and current Ir at one end of the line. The other end of the line may be connected to a load which may be another AC power connection.
The voltage Vr (known as the xe2x80x9crelaying voltagexe2x80x9d) is related to the current Ir (known as the xe2x80x9crelaying currentxe2x80x9d) by the equation:
Vr=IrZxe2x80x83xe2x80x83(1)
Since the relaying voltage and current are known by measurement, a value for Z can be calculated and, if the line impedance parameters per unit-length are known, an indication can be derived as to whether the fault lies within the particular section of line being monitored by the relaying equipment.
Discrete signal processing techniques allow calculation of Z in terms of R and L using the equation:                               v          r                =                              Ri            r                    +                      L            ⁢                                          ⅆ                                  i                  r                                                            ⅆ                t                                                                        (        2        )            
The use of the differential equation (2) rather than the phase equation (1) removes the need for the relay input signals vr and ir to be at a specified frequency. Thus equation (2) could be equally valid when applied to a 50 Hz or 60 Hz system, so that R and L could in principle be solved over a range of discrete time-signal frequencies of the relay inputs vr and ir.
The value of shunt capacitance present in overhead lines is sufficiently low to be neglected at power-system frequency so that equation (2) can be used to determine the values of R and L. However, the presence of capacitance causes high-frequency travelling waves to be generated when a fault occurs and these can cause errors in the calculation of R and L. It is therefore necessary to remove the travelling-wave frequencies from the signals vr and ir before calculating R and L using equation (2). Since these frequencies are relatively high with respect to the power-system frequency, they can be removed by short-window digital filters without causing the relay operating time to be extended beyond one power-frequency cycle.
On cable circuits, however, the values of shunt capacitance are much greater and the travelling-wave noise is far lower in frequency, so that its effects are less easily removed by filtering. On this basis the values of R and L calculated from equation (2) no longer accurately represent the location of the fault.
In accordance with the invention, there is provided relay equipment for an electrical power line, characterized by fault-detection means comprising:
a signal-deriving means for deriving first and second signals representative of a voltage and current, respectively, at a first end of said line;
a calculating means for calculating from said first and second signals and from defined values of series and shunt parameters of said line a value of voltage and current associated with a point along said line intermediate said first end and a second end of said line; and
a fault-location determining means for determining from said calculated voltage and current values whether a fault lies between said first end and said intermediate point.
The calculating means may calculate said intermediate-point voltage and current values using a value of a derivative of said second signal with respect to time, and preferably employing the matrix relationship:       [                                        v            1                                                            i            1                                ]    =            [                                    1                                              -                              (                                                      R                    0                                    +                                                            L                      0                                        ⁢                                          ⅆ                                              ⅆ                        t                                                                                            )                                                                                                        -                                  C                  0                                            ⁢                              ⅆ                                  ⅆ                  t                                                                          1                              ]        ⁢          xe2x80x83        [                                        v            0                                                            i            0                                ]  
where v1, i1 are said voltage and current at said intermediate point, v0, i0 are said voltage and current at said first end of the line, R0 and L0 are said series parameters of the line and C0 is a shunt parameter of the line.
The calculating means may be arranged to model said line as a plurality p of line-portions in series having respective series and shunt parameters, said matrix relationship being:       [                                        v            1                                                            i            1                                ]    =            ∏              m        =        1            p        ⁢          xe2x80x83        ⁢                  [                  xe2x80x83                ⁢                                            1                                                      -                                  (                                                            R                                              0                        ⁢                        m                                                              +                                                                  L                                                  0                          ⁢                          m                                                                    ⁢                                              ⅆ                                                  ⅆ                          t                                                                                                      )                                                                                                                          -                                      C                                          0                      ⁢                      m                                                                      ⁢                                  ⅆ                                      ⅆ                    t                                                                                      1                                      ⁢                  xe2x80x83                ]            ⁢              xe2x80x83            [                                                  v              0                                                                          i              0                                          ]      
Corresponding parameters of said line-portions may have substantially the same value.
The line may be composed of a plurality q of sections in series having respective series and shunt parameters, each of said plurality q of sections being composed of a plurality p of line-portions in series having respective series and shunt parameters, said matrix relationship being:       [                                        v            q                                                            i            q                                ]    =            ∏              n        =        0                    q        -        1              ⁢          xe2x80x83        ⁢                  ∏                  m          =          1                p            ⁢              xe2x80x83            ⁢                        [                      xe2x80x83                    ⁢                                                    1                                                              -                                      (                                                                  R                                                  n                          ⁢                                                      xe2x80x83                                                    ⁢                          m                                                                    +                                                                        L                                                      n                            ⁢                                                          xe2x80x83                                                        ⁢                            m                                                                          ⁢                                                  ⅆ                                                      ⅆ                            t                                                                                                                )                                                                                                                                            -                                          C                                              n                        ⁢                                                  xe2x80x83                                                ⁢                        m                                                                              ⁢                                      ⅆ                                          ⅆ                      t                                                                                                  1                                              ⁢                      xe2x80x83                    ]                ⁢                  xe2x80x83                [                                                            v                0                                                                                        i                0                                                    ]            
At least the shunt parameters of said sections may not all be of substantially the same value. The sections may correspond to respective distinct forms of line including at least one overhead line section and at least one cable section.
Each of said line or line-portions is preferably modelled by said calculating means as a xcex93-network, though a xcfx80-network may also be employed.
The fault-location determining means may comprise means for detecting whether said voltage at said intermediate point is zero, positive or negative relative to a reference quantity, a zero result indicating that there is a fault at said intermediate point, a positive result indicating that there is a fault between said point and one end of said line and a negative result indicating that there is a fault between said point and the other end of said line. The reference quantity may be the current associated with said intermediate point.
The calculating means may comprise means for calculating from said calculated voltage and current values a value of a complex impedance between said first end and said intermediate point, and said fault-location determining means may comprise means for evaluating a sign of said complex impedance. The calculating means may calculate said value of a complex impedance by means of the equation:   v  =      Ri    +          L      ⁢                        ⅆ          i                          ⅆ          t                    
where v and i are said intermediate-point voltage and current values, respectively, and R and L are components of said complex impedance.
A negative result may indicate that there is a fault between said intermediate point and said first end of said line and a positive result indicate that there is a fault between said intermediate point and said second end of said line.
The intermediate point will usually lie approximately 80% of the way along said line from said first end of the line.
The signal-deriving means may be adapted to derive said first and second signals both before and after the occurrence of a fault on said line, said calculating means may be adapted to calculate from said pre-fault and post-fault first and second signals and from said parameters and from a value of a source impedance of said second end of said line a change in a value of voltage and current associated with said intermediate point and to calculate from said change a value of a complex impedance existing between said intermediate point and a reference point, and said fault-location determining means may be adapted to determine a sign of an imaginary part of said complex impedance and to infer from said sign a position of said fault relative to said intermediate point.
In accordance with a second aspect of the present invention, a method of determining if a fault on a power line lies within a particular zone of said line comprises the steps of:
measuring a voltage and current at a first end of said line before and after the occurrence of a fault;
calculating the complex impedance between a point on said line intermediate said first end and a second end of the line and a reference point, said complex fault impedance calculation utilizing the measured voltage and current values and values relating to parameters of the line and to a source impedance at said second end of the line;
determining a sign of an imaginary part of said complex impedance; and
inferring from said sign a position of said fault relative to said intermediate point on said line.
The inference of said fault position may follow the rule that a negative sign indicates a fault between one of said ends and said intermediate point of said line, a positive sign indicates a fault between the other of said ends and said intermediate point of said line and a zero imaginary part indicates a fault at said intermediate point itself.
The step of calculating the complex impedance may comprises a calculation of the voltage and current at said intermediate point using the equation:       [                                        v            1                                                            i            1                                ]    =            [                                    1                                              -                              (                                                      R                    0                                    +                                                            L                      0                                        ⁢                                          ⅆ                                              ⅆ                        t                                                                                            )                                                                                                        -                                  C                  0                                            ⁢                              ⅆ                                  ⅆ                  t                                                                          1                              ]        ⁢          xe2x80x83        [                                        v            0                                                            i            0                                ]  
where v0, i0 are the voltage and current at said first end of the line, v1, i1 are the voltage and current at said intermediate point and R0, L0 are series parameters and C0 is a shunt parameter of said line.
The line may be divided into a plurality q of sections and said step of calculating the complex impedance may comprise a calculation of a voltage and current at said intermediate point using the equation:       [                                        v            q                                                            i            q                                ]    =            ∏              n        =        0                    q        -        1              ⁢          xe2x80x83        ⁢                  [                  xe2x80x83                ⁢                                            1                                                      -                                  (                                                            R                      n                                        +                                                                  L                        n                                            ⁢                                              ⅆ                                                  ⅆ                          t                                                                                                      )                                                                                                                          -                                      C                    n                                                  ⁢                                  ⅆ                                      ⅆ                    t                                                                                      1                                      ⁢                  xe2x80x83                ]            ⁢              xe2x80x83            [                                                  v              0                                                                          i              0                                          ]      
where v0, i0 are the voltage and current at said first end of the line, vq, iq are the voltage and current at said intermediate point and Rn, Ln are series parameters and Cn is a shunt parameter of respective said sections of the line.
The line or each of said sections may be conceptually subdivided into p line-portions having respective line parameters, and said step of calculating the complex impedance may comprise a calculation of a voltage and current at said intermediate point using the equation:       [                                        v            q                                                            i            q                                ]    =            ∏              n        =        0                    q        -        1              ⁢          xe2x80x83        ⁢                  ∏                  m          =          1                p            ⁢              xe2x80x83            ⁢                        [                      xe2x80x83                    ⁢                                                    1                                                              -                                      (                                                                  R                                                  n                          ⁢                                                      xe2x80x83                                                    ⁢                          m                                                                    +                                                                        L                                                      n                            ⁢                                                          xe2x80x83                                                        ⁢                            m                                                                          ⁢                                                  ⅆ                                                      ⅆ                            t                                                                                                                )                                                                                                                                            -                                          C                                              n                        ⁢                                                  xe2x80x83                                                ⁢                        m                                                                              ⁢                                      ⅆ                                          ⅆ                      t                                                                                                  1                                              ⁢                      xe2x80x83                    ]                ⁢                  xe2x80x83                [                                                            v                0                                                                                        i                0                                                    ]            
The intermediate point may lie approximately 80% of the way along the line from said first end thereof.